To understand the linguistic landscape of France in the 9th century, it's essential to look at the history of the Franks and the establishment of the Frankish Empire. First, let's distinguish between Franks, because there is scarcely another ethnonym that has been used more extensively to refer to vastly different peoples:

1. The Franks that the Romans first describe in the 3rd-century CE are a tribal confederacy made up out of a number of smaller Germanic tribes that had been living around the Imperial northwestern frontier for centuries.
2. The Franks of the Late Merovingian / (post) Carolingian period are a Western European ruling class essentially the result of a mixing between the earlier Germanic tribal elites and the Gallo-Roman aristocracy.

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It's the first group that settles much of the Roman provinces of Germania Inferior and Gallia Belgica during the 4th century and later takes over northern Gaul.

Their linguistic influence is both remarkable and limited. It's remarkable because (together with the Anglo-Saxons) the Franks are the only Germanic people to have kept their language after settling within the Roman Empire. However, they only did so in the area they settled rather than conquered: the Low Countries and the far northwestern tip of France. Frankish elites and their followings did settle in Gaul (Northern and Central France) but they were eventually assimilated by the surrounding and more numerous Gallo-Roman populations. The Franks had longstanding contacts with Rome prior to their migration and would have already been familiar with Latin-speakers, especially those previously employed as auxilia/mercenaries by Rome or merchants. With this in mind, it shouldn't come as much as a shock that even a Frankish ruler as early as Clovis (466 - 511) is commonly assumed to have been effectively bilingual, speaking both a Germanic dialect and a Romance vernacular.

During Clovis' time, the Franks are no longer migrating as a tribe: Clovis is a warlord with an army, not the leader of a people on the move and this is reflected in his politics and those of his successors. The marriage politics of the Merovingian elite show that they are looking far across their initial tribal lands to forge alliances, both with other Germanic warlords across the Rhine and with native Gallo-Roman potentates. Their considerations were focused on power and status, not on language. Bilingualism among the elites would have been the norm (especially within the traditional core of the Frankish Empire, roughly the triangle between Tournai, Reims and Aachen) not the exception.

In the divisions of the 9th century however, the core area would become part of the Middle Kingdom which was subsequently attacked and divided between West and East Francia. Ultimately, rather than forming the heartlands, the former core area essentially became the periphery of both remaining realms. This shifted the linguistic dynamics. West Francia had a limited settled Germanic speaking populace (which was relatively small and geographically contained) whereas East Francia was generally Germanic speaking, though with large internal differences. The Oaths of Strasbourg are essentially the embodiment of this new linguistic reality: the elites who signed them were bilingual, most of their vassals now tended not to be or less so.

This development had a dramatic effect on the Frankish language. In France, it ceased being spoken by the 11th century; having already being delegated to a secondary status within the elite framework of bilingual. In what was to become Germany, the Frankish dialects were essentially assimilated by the various High German varieties. Only in the Low Countries did the Frankish language hold on, over time developing into Dutch, and the language border between French and Dutch can be seen as a rough indication of where the Frankish settlers were able to maintain/impose their language, either due to numerical superiority or depopulation prior to settling there.

It is impossible to say, when the exact shift to monolingualism among the Kings of West Francia / France occurred, but it is safe to assume that the primacy of Old French / Gallo Roman within the bilingual framework had been firmly established somewhat prior to the Oaths of Strasbourg, after which Germanic-Romance bilingualism would rapidly become a local affair.

TL, DR

Frankish elites had been bilingual since the 6th century onward. It is during the 9th century that this bilingualism starts to disappear, with Frankish being extinct in most of France by the early 11th century.